Objectives:

1
Hedging Foreign Exchange Risk

• Objectives
• Consider how foreign exchange (FX) risk can be
  hedged with forward exchange contracts.
• Analyze how the absence of arbitrage determines
  the forward exchange rate (Covered Interest
  Parity).
• Consider how currency swaps can be used to hedge
  periodic foreign currency payments.
• Understand how FX options can insurance against
  FX risk.

2

• Many FIs have multi-national operations. A FIs
  customers who reside or do business in a foreign
  country may desire a financial service that
  results in the creation of a foreign currency
  denominated asset or liability for the FI.
  Examples
• A U.S. finance company makes a yen-denominated
  loan to a Japanese company.
• The London branch of a French bank accepts a
  pound- denominated deposit from a U.K. resident.
• A Dutch insurance company underwrites a life
  insurance policy for a U.S. resident that is
  denominated in dollars.
• A U.S. investment bank provides euro-denominated
  bridge-loan financing for a merger of two Italian
  firms.
• A British pension fund invests in Canadian dollar
  denominated bonds.

3

• If a FIs foreign currency denominated assets are
  not matched with offsetting foreign currency
  denominated liabilities, the FIs net worth will
  be exposed to foreign exchange (FX) risk an
  appreciation or depreciation of the foreign
  currency.
• Example A U.S. bank has offices in London and
  negotiates a 1,000,000 one-year loan to a
  credit-worthy U.K. firm at an interest rate of
  7.5.
• At the current spot exchange rate of S0
  1.6715/, this requires funding of 1,671,500
  that the bank raises by issuing a one-year dollar
  denominated C.D. at an interest rate of 5.5.

4

• Since the pound-denominated loan interest rate is
  7.5 , the bank will receive 1,075,000 at the
  end of the year. But if the depreciates
  vis-à-vis the during this time, the U.S. bank
  could suffer a lost when converting s for s
  at year-end.
• This is because the end-of-year value of the
  loan will be
• Maturity value of loan 1,075,000 x S1
• where S1 is the random end-of-year spot /
  exchange rate. Indeed, the value of the loan
  repayment could be less than the banks payment
  on its CD of 1,671,500 x (1.055) 1,763,432.50
  resulting in a loss on the transaction. This
  would occur if

5
Hedging with FX Forward Contracts

• To hedge its exposure, the bank could take a
  short position in a one-year forward contract on
  1,075,000. Suppose that the current one-year
  forward exchange rate (forward price) for trading
  pounds and dollars is f0 1.6441/.
• Thus, the maturity value of the banks loan plus
  the maturity value of its short forward position
  is

Maturity Value of Short Position Forward
Price of s
- Spot Market Price of
s
1,075,000 x 1.6441/ - 1,075,000 x S1
1,767,407.50 - 1,075,000 x S1
Banks end-of-year investment value 1,075,000
x S1 1,767,407.50 - 1,075,000 x S1
1,767,407.50
6

• Essentially, these transactions enable the bank
  to satisfy its short forward position by
  delivering 1,075,000 (its loan payment) in
  exchange for receiving 1,767,407.50.

Bank Balance Sheet Assets
Liabilities One-Year Loan
One-Year CD (1,075,000)
(1,763,432.50)
Off-Balance Sheet Forward
Contract Assets Liabilities
Receive Forward Price Deliver
to Long Party (1,767,407.50)
(1,075,000)
7

• Note that the loan and forward transactions
  result in the bank earning a risk-free one-year
  U.S. interest rate of
• which exceeds the 5.5 interest rate it must pay
  on its CD. Hence, this forward exchange hedging
  guarantees that the bank will make a profit on
  its lending to the U.K. firm.
• Forward exchange contracts such as this comprise
  the single largest derivative market. It is an
  over-the-counter market consisting of dealers
  employed by large, international banks.
• Derivatives with very similar hedging properties
  are FX futures contracts that are traded on
  exchanges such as the CME and FINEX. Dealers of
  forward exchange contracts often use these FX
  futures to hedge their positions.

8
Covered Interest Parity

• In the previous example, we took the one-year
  forward exchange price (rate) of f0 1.6441/
  as given. Let us next investigate the
  determinants of such forward exchange rates.
• As before, let S0 be the current spot foreign
  exchange rate in American terms, that is, in
  per foreign currency. For example, if the
  foreign currency is the euro () then on
  4/7/2004, S0 1.2175/. Now consider the
  payoff to a long position in a forward exchange
  contract that matures at date ?. At date ? the
  long party pays f0 in return for receiving one
  worth S?. Hence, the payoff can be written as
• Payoff at date ? to long party
  S? - f0
• This payoff can be replicated by borrowing in
  dollars and investing in euro bonds. The two
  actions taken at date 0 are

9
1) Borrow f0 /(1i)? at the date 0 U.S.
risk-free interest rate of i. 2) Purchase a euro
bond having a date ? face value of 1. If the
date 0 euro interest rate is i, the cost of
this investment is S0/(1 i)?.

• Actions 1) and 2) produce a net cash flow at
  date ? of
• Euro Bond Return - U.S Borrowing
  Repayment
• S?(1 i)? /(1 i)? - f0
  (1i)? /(1i)? S? - f0

which is exactly the payoff of the long forward
position. Hence, the Law of One Price states
that the value of the forward contract to the
long party, PVforward, must be the present values
of trades 1) and 2)
10

• When the forward exchange contract is initiated,
  its value equals zero since the long and short
  parties agree to it voluntarily and no initial
  payments are made. The forward exchange rate,
  f0, adjusts to make the contract fair.
  Therefore, setting PVforward 0 and solving for
  f0, we obtain
• which is the Covered Interest Parity condition.
  It shows that rates in four markets are linked
  the forward exchange rate, the spot exchange
  rate, the U.S. money market rate, the Euro money
  market rate. Trading in any three of these
  markets can replicate the fourth.

11
Example The current Japanese yen per euro spot
exchange rate is 115.69/. The annualized,
semi-annually compounded interest rates for
borrowing or lending for six-months in euros and
Japanese yen are 3.80 and 0.16 ,
respectively. According to Covered Interest
Parity, what is the six-month forward exchange
rate in yen per euro (/ )?
12
Currency Swaps

• A currency swap is an agreement between two
  parties to exchange payments in one currency for
  payments in another.
• In a fixed-fixed currency swap, parties agree to
  exchange a pre-agreed amount of foreign currency
  for domestic currency at specific future dates.
• Example A Japanese investment bank issues a 10
  m., 7-year euro-denominated bond in Frankfurt.
  The bond makes annual coupon payments of 4 , or
  400,000 per year. After two years, the
  Japanese bank wishes to reduce its
  euro-liabilities because its euro-denominated
  assets have declined or because it fears that the
  euro will appreciate vis-à-vis the yen.

13

• To convert its euro-denominated bond into a
  yen-denominated one, it agrees to a 5-year
  currency swap in which it contracts to pay yen
  and receive euros.
• If the current swap rate for a five-year yen for
  euro swap is 100/, then over the next five
  years the bank would make annual (coupon)
  payments of 40 m. in exchange for receiving
  annual payments of 400,000. In addition, in
  the final fifth year the swap would require that
  the bank make a principal payment of 1,000 m.
  in exchange for 10 m.

Bank Balance Sheet Assets
Liabilities Five-year -
denominated Bond
Off-Balance Sheet
Currency Swap Assets
Liabilities Swap Payments
Swap Payments
14

• This currency swap is equivalent to five
  different forward exchange contracts to deliver
  euros for yen made at the same forward exchange
  rate of f0 100/.
• Thus, if S0 is the current / spot exchange
  rate, i(? ) is the interest rate for borrowing
  or lending in euros from date 0 to date ? and
  i(? ) is the interest rate for borrowing or
  lending in yen from date 0 to date ? , then the
  swaps value to the party delivering (short)
  euros is

15

• When the swap is first initiated by the two
  parties, PVswap 0. Given S0, i(? ), and i(?
  ) for ? 1,,5, the five-year swap rate f0 is
  determined such that PVswap 0, e.g., f0
  100/.
• Similar to interest rate swaps, currency swaps
  are sold by FX dealers in the over-the-counter
  market.
• Swaps can be arranged that combine the features
  of both currency and interest rate swaps. A
  fixed-floating currency swap involves exchanging
  fixed-interest payments in one currency for
  floating-rate interest payments in another.
• For example, if in the previous example, the
  Japanese bank had issued a euro-denominated
  floating-rate bond tied to one-year euroLIBOR, it
  could become a fixed yen payer, euroLIBOR
  receiver in a 5-year fixed-floating swap.

16
FX Options

• Options on foreign currencies can be used to
  insure against a foreign currency depreciation.
• Example A U.S. pension fund purchases a
  six-month pound- denominated C.D. from a British
  bank that pays 1,000,000 in six-months.
• After three months, the pension fund fears that
  the Fed will soon raise U.S. interest rates which
  would likely lead to an significant appreciation
  of the dollar vis-à-vis the pound from the
  current spot exchange rate of S0 1.8405/.
• To insure against this pound depreciation, the
  pension fund purchases three-month maturity put
  options on 1 m. with an exercise price of X
  1.8300/.

17

• The maturity value of these put options are
• Put option payoff max X
  S? m., 0
• 
  max1.83 m. S? m., 0
• Combining these put options with its pound-
  denominated C.D. implies
• Put option CD payoff max1.83 m. S?
  m., 0 S? m.
• 
  max1.83 m., S? m.
• so that its insured CD payment will be no less
  than 1.83 m.
• Of course the pension fund must pay an initial
  premium to the writer of the option for this
  insurance (e.g., 0.04/) or 40,000.
• Note that this put option on the pound is
  equivalent to a call option on the dollar. It
  pays off when the dollar appreciates (pound
  depreciates).